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Research Papers

Low Velocity Impact of Flat and Doubly Curved Polycarbonate Panels

[+] Author and Article Information
G. O. Antoine

Department of Biomedical Engineering and
Mechanics (M/C 0219),
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: antoineg@vt.edu

R. C. Batra

Fellow ASME
Department of Biomedical
Engineering and Mechanics (M/C 0219),
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: rbatra@vt.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 10, 2014; final manuscript received February 7, 2015; published online February 26, 2015. Assoc. Editor: Weinong Chen.

J. Appl. Mech 82(4), 041003 (Apr 01, 2015) (21 pages) Paper No: JAM-14-1515; doi: 10.1115/1.4029779 History: Received November 10, 2014; Revised February 07, 2015; Online February 26, 2015

Three-dimensional finite transient deformations of polycarbonate (PC) panels impacted at low velocity by a hemispherical-nosed rigid cylinder have been studied by using the commercial finite element software ls-dyna with a thermo–elasto–viscoplastic material model for the PC incorporated in it as a user defined subroutine. The implementation of the subroutine has been verified by comparing analytical and numerical solutions of simple initial-boundary-value problems. The mathematical model of the low velocity impact problem has been validated by comparing the computed and the experimental results for the maximum deflection and time histories of the centroidal deflection. It is found that the initial slope of the reaction force between the impactor and the panel versus the indentation for a curved panel can be nearly 20 times that for the flat panel of the same thickness as the curved panel. For the impact velocities considered, it is found that the maximum effective plastic strain in the PC shell near the center of impact and the dominant deformation mode there strongly depend on the panel curvature, the panel thickness, and the impact speed. Effects of the panel curvature, the panel thickness, and the impact speed on stresses and strains developed in a panel are delineated. This information should help designers of impact resistant transparent panels such as an airplane canopy, automobile windshield, and goggles. However, damage initiation and propagation, and the final indentation induced in the clamped panels have not been computed.

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Figures

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Fig. 1

Sketch of the impact problem studied

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Fig. 2

Effective true stress versus effective true strain for uniaxial tension, simple shear, and uniaxial compression of the PC at 5000/s true strain rate

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Fig. 3

Analytical and computed reaction forces (solid lines) and the % difference between them (dashed line) as a function of the indentation

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Fig. 4

Time histories of the deflection (experimental data from Ref. [33]) of the centroid of the back surface of two panels for different impact velocities

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Fig. 5

Deformed shapes at different times of the back surface of the 5.60 mm thick PC panel impacted at 30.5 m/s. Experimental data from Ref. [31].

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Fig. 6

Average axial stress and difference between the average axial stress on the top and the bottom surfaces as a function of the x-coordinate along the centroidal axis for impact at 30 m/s of panels of different thicknesses

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Fig. 7

Fringe plots of the effective plastic strain in the deformed configurations corresponding to times when plates first revert back to the zero deflection position

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Fig. 8

Time histories of the energy dissipated, the strain (elastic) energy, the kinetic energy, and the contact force of plates of different thicknesses impacted at 30 m/s

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Fig. 9

Axial stress and axial stretch as a function of the distance from the plate center at the top, the mid- and the bottom surfaces of the 5.85 mm thick plate for 30 m/s impact velocity at the time tf = 2.60 ms

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Fig. 10

Through-the-thickness variation of the axial stretch and the axial stress on the centroidal axis for the 3, 4.45, 5.85, 9.27, and 12.32 mm thick plates and 30 m/s impact velocity at the times tf of Fig. 7

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Fig. 11

Average axial stress and difference between the average axial stress on the top and the bottom surfaces as a function of the X-coordinate along the centroidal axis for impact of the 5.85 mm thick panel at different speeds

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Fig. 12

Fringe plots of the effective plastic strain in the deformed configurations at the times of separation between the 5.85 mm thick plate and the impactor. The times of separation are also listed.

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Fig. 13

Time histories of the normalized energy dissipated, the normalized strain (elastic) energy, the normalized kinetic energy, and the contact force for the 5.85 mm thick plate for different impact speeds. Energies are normalized by the initial kinetic energy of the impactor.

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Fig. 14

Axial stress and axial stretch as a function of the distance from the plate center at the top, midplane, and bottom of the PC plate for 50 m/s impact velocity and at the final time tf = 2.40 ms

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Fig. 15

Axial stretch and axial stress at the plate center as a function of the initial Z position for 10, 20, 30, 40, and 50 m/s impact speeds at the times tf of Fig. 12

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Fig. 16

Contact force versus indentation for the (a) 3.00, (b) 4.45, (c) 5.85, (d) 9.27, and (e) 12.32 mm thick panels of different radii of curvature

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Fig. 17

Average axial stress and the difference between the axial stress on the top and on the bottom surfaces of the (a) 3.00, (b) 4.45, (c) 5.85, (d) 9.27, and (e) 12.32 mm thick panels as a function of the initial arc length (measured from the panel center)

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Fig. 18

Time histories of the contact force for 3 mm thick panels of different curvatures impacted at 20 m/s

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Fig. 19

Fringe plots of the effective plastic strain in the central region of a cross section passing through the centroid of the 3 mm thick panels with (a) R > 0 and (b) R < 0. Note that values of fringes in Figs. (a) and (b) are different.

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Fig. 20

Time histories of the energy dissipation for 3 mm thick panels of different curvatures for impacts at 20 m/s

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Fig. 21

Fringe plots of the energy dissipation density on the back surface and through the thickness of panels with R = 508 and 127 mm

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Fig. 22

Variation of the energy dissipation represented by the function f(r) with the radius for the flat and the curved panels of R = 127 and 508 mm. The figure in the right is a blow-up of that on the left for small values of r.

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Fig. 23

Average axial stress and the difference between the axial stress on the top and on the bottom surfaces of the (a) 3 mm, (b) 4.45 mm, (c) 5.85 mm, (d) 9.27 mm, and (e) 12.32 mm thick panels as a function of the initial arc length (measured from the panel center)

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Fig. 24

Fringe plots of the effective plastic strain in the central region of a cross section passing through the centroid of the 12.32 mm thick panels with (a) R > 0 and (b) R < 0

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Fig. 25

Axial stress and axial stretch as a function of the distance from the plate center at the top, midplane, and bottom of the (a) 3.00 mm and (b) 12.32 mm thick plates for 50 m/s impact speed when the impactor separates from the plate

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Fig. 26

Through the thickness variations of the axial stretch and the axial stress on the transverse normal passing through the plate centroid for 20 m/s impact velocity at the time when the impactor separates from the plate

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Fig. 27

Variation with the strain rate and temperature of the total Young's modulus (Eα + Eβ) of the PC

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Fig. 28

Coarse mesh for the impactor and the square plate (much finer meshes were used for the simulations)

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